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Parameter estimation of inverse Weibull distribution under competing risks based on the expectation-maximization algorithm

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2024年第7期40卷 3795-3808页

作者： Alotaibi, Refah Rezk, Hoda Park, Chanseok Princess Nourah bint Abdulrahman Univ Coll Sci Dept Math Sci Riyadh Saudi Arabia Al Azhar Univ Dept Stat Cairo Egypt Pusan Natl Univ Dept Ind Engn Appl Stat Lab Busan 46241 South Korea

A system consisting of interconnected components in series is under consideration. This research focuses on estimating the parameters of this system for incomplete lifetime data within the framework of competing risks, employing an underlying inverse Weibull distribution. While one popular method for parameter estimation involves the Newton-Raphson (NR) technique, its sensitivity to initial value selection poses a significant drawback, often resulting in convergence failures. Therefore, this paper opts for the expectation-maximization (em) algorithm. In competing risks scenarios, the precise cause of failure is frequently unidentified, and these issues can be further complicated by potential censoring. Thus, incompleteness may arise due to both censoring and masking. In this study, we present the em-type parameter estimation and demonstrate its superiority over parameter estimation based on the NR method. Two illustrative examples are provided. The proposed method is compared with the existing Weibull competing risks model, revealing the superiority of our approach. Through Monte Carlo simulations, we also examine the sensitivity of the initial value selection for both the NR-type method and our proposed method.

关键词： censoring competing risks em algorithm inverse Weibull masking

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Range-based volatility modeling in financial markets using a family of scale mixtures of Birnbaum-Saunders distribution

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第10期53卷 4956-4975页

作者： Tamandi, Mostafa Desmond, Anthony F. F. Jamalizadeh, Ahad Vali E Asr Univ Rafsanjan Dept Stat Rafsanjan Iran Univ Guelph Dept Math & Stat Guelph ON Canada Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

We propose scale mixtures of Birnbaum-Saunders distributions as a new class of positive skewed and leptokurtic distributions and use it to model volatility in stock markets. To estimate the model parameters, we develop an Expectation-Conditional-Maximization algorithm. The numerical performance of the proposed methodology is evaluated by means of Monte Carlo simulations. Application of the new model in volatility modeling is illustrated with some real-life data.

关键词： Birnbaum-Saunders em algorithm Range-based volatility Scale mixtures

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Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents

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SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS-METHODS 2025年第1期5卷

作者： Ando, Yasunobu Kasamatsu, Shusuke Iwasaki, Suguru Tanaka, Yumi Tokyo Inst Technol Inst Innovat Res Lab Chem & Life Sci Nagatsuta ChoMidori Ku Yokohama 2268501 Japan Yamagata Univ Fac Sci Acad Assembly Yamagata Yamagata Japan Tokyo Univ Sci Fac Engn Dept Ind Chem Tokyo Japan

We propose a theoretical formalism for inferring the parameters of non-negative physical models via statistical divergence to generalise the fitting process beyond conventional methods. For example, we show that minimising L2 and Kullback-Leibler divergence is equivalent to least squares and maximum likelihood estimation, respectively, for the parameters of non-negative physical models like a probability distribution. To demonstrate this formalism, parameters were estimated in a theoretical model of the thermally stimulated depolarisation current (TSDC), which has a non-negative but complex exponential form. Some technical aspects were also discussed as key points to enable high-throughput fitting of multimode models of TSDC using the proposed formalism, such as the use of the peak temperature as a fitting parameter, which is easily estimated from measured data, instead of a pre-exponential factor that varies by orders of magnitude, and the use of the generalised exponential integral function to speed up the fitting algorithm.

关键词： Machine learning em algorithm thermally stimulated depolarization currents statistical divergence maximum likelihood estimation non-linear regression

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Speed Prediction Based on a Traffic Factor State Network Model

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTemS 2021年第5期22卷 3112-3122页

作者： Zhang, Weibin Feng, Yaoyao Lu, Kai Song, Yuhang Wang, Yinhai Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China South China Univ Technol Sch Civil Engn & Transportat State Key Lab Subtrop Bldg Sci Guangzhou 510640 Peoples R China Univ Washington Dept Civil & Environm Engn Seattle WA 98195 USA

The rapid development of traffic theory and information technology has provided diversified and large-scale traffic data resources for traffic research and urban traffic management. At the same time, these data also present many challenges, such as missing data and deviations in data collection. Many researchers have reported that inaccurate or incomplete measurements of traffic variables can be corrected based on either traditional traffic flow theory, which ignores the randomness of traffic, or are performed using machine learning methods, which emphasize data quantity, but do not make effective use of domain knowledge. This paper proposes a Traffic Factor State Network framework defined by traffic factors and their links to represent the relationships between traffic factors;this framework includes not only obvious traffic factors like volume and speed, but also hidden traffic factors such as the environmental impact factor, which is a variable used to represent complex road conditions. This variable is used to describe the influence of non-traffic flow parameters such as road condition and environmental factors, and is estimated by the em (Expectation Maximization) algorithm based on historical data. This study used a high-order multivariate Markov model to implement the TFSN, which was then used to establish a stochastic model of speed and related factors. A large amount of historical data was used to calculate and calibrate the strength of the links between the model factors. Finally, a stochastic model of speed prediction was established. The verification results compared with actual cases demonstrate the validity and applicability of the proposed model.

关键词： Roads Data models Predictive models Solid modeling Markov processes Traffic factor state network speed prediction high-order Markov chain environmental impact factor em algorithm

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Non parametric observation-driven hidden Markov model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年

作者： Bacave, Hanna Cheptou, Pierre-Olivier Limnios, Nikolaos Peyrard, Nathalie Univ Toulouse INRAE UR MIAT Castanet Tolosan France CNRS CEFE Montpellier France Univ Technol Compiegne Sorbonne Univ Alliance LMAC Compiegne France

Hidden Markov models (HMM) are used in different fields to study the dynamics of a process that cannot be directly observed. However, in some cases, the structure of dependencies of a HMM is too simple to describe the dynamics of the hidden process. In particular, in some applications in finance and in ecology, the transition probabilities of the hidden Markov chain can also depend on the current observation. In this work, we are interested in extending the classical HMM to this situation. We refer to the extended model as the observation-driven hidden Markov model (OD-HMM). We present a complete study of the general non parametric OD-HMM with discrete and finite state spaces. We study its identifiability and the consistency of the maximum likelihood estimators. We derive the associated forward-backward equations for the E-step of the em algorithm. The quality of the procedure is tested on simulated datasets. We illustrate the use of the model on an application focused on the study of annual plant dynamics. This work establishes theoretical and practical foundations for this framework that could be further extended to the parametric context in order to simplify estimation and to hidden semi-Markov models for more realism.

关键词： Non homogeneous HMM identifiability consistency em algorithm

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The expectation-maximization algorithm for autoregressive models with normal inverse Gaussian innovations

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第11期53卷 5421-5441页

作者： Dhull, Monika S. Kumar, Arun Wylomanska, Agnieszka Indian Inst Technol Ropar Dept Math Rupnagar India Wroclaw Univ Sci & Technol Fac Pure & Appl Math Hugo Steinhaus Ctr Wroclaw Poland Indian Inst Technol Ropar Dept Math Rupnagar 140001 Punjab India

In this paper, we study the autoregressive (AR) model with normal inverse Gaussian (NIG) innovations. The NIG distribution is semi heavy-tailed and is helpful in capturing the extreme observations present in the data. The expectation-maximization (em) algorithm is used to estimate the parameters of the considered AR(p) model. The efficacy of the estimation procedure is shown on the simulated data for AR(2) and AR(1) models. A comparative study is presented, where the classical estimation algorithms are also incorporated, namely, Yule-Walker and conditional least squares methods along with em method for model parameter estimation. In simulation study, the maximum likelihood estimation (MLE) of NIG distribution by em algorithm and iterative Newton-Raphson method are also compared. The real-life applications of the introduced model are demonstrated on the NASDAQ stock market index data and US gasoline price data. The studies show that AR(1) model with NIG residuals is good fit for financial data with extreme values as well as for gasoline price data.

关键词： Normal inverse Gaussian distribution Autoregressive model em algorithm Monte Carlo simulations

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Integrative Clustering Analysis with Application in Multi-Source Gene Expression Data

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Journal of Data Science 2022年第1期20卷 14-33页

作者： Yang, Liuqing Pan, Qing Zhao, Yunpeng Department of Statistics George Washington University Washington DC United States School of Mathematical and Natural Sciences Arizona State University Tempe AZ United States

In omics studies, different sources of information about the same set of genes are often available. When the group structure (e.g., gene pathways) within the genes are of interests, we combine the normal hierarchical model with the stochastic block model, through an integrative clustering framework, to model gene expression and gene networks jointly. The integrative framework provides higher accuracy in extensive simulation studies when one or both of the data sources contain noises or when different data sources provide complementary information. An empirical guideline in the choice between integrative versus separate clustering models is proposed. The integrative clustering method is illustrated on the mouse embryo single cell RNAseq and bulk cell microarray data, which identified not only the gene sets shared by both data sources but also the gene sets unique in one data source. © 2022 Center for Applied Statistics, School of Statistics, Renmin University of China. All rights reserved.

关键词： em algorithm empirical guidelines microarray data normal hierarchical model single cell RNAseq stochastic block model

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Analysis of Failure Data with Missing Labels 4

Analysis of Failure Data with Missing Labels

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4th International Conference on System Reliability and Safety Engineering (SRSE)

作者： Cai, Jiaxiang Ye, Xin Tang, Loon Ching Natl Univ Singapore Dept ISEM Singapore Singapore

ISBN: (纸本)9781665473880

This paper presents a new technique for the analysis of failure data when some of the labels are missing. When multiple systems are in operation, the label associated with a failure are usually given to indicate the system type or the specific system the failure belongs to. Data records in practice often suffer from missing labels. Missing labels can be partially known or completely unknown. A statistical inference procedure based on the expectation maximization algorithm is proposed to address this problem. Give the observed data, the proposed technique derives explicitly the distribution of the missing labels. The advantage of this technique is that it is a general inference procedure and is flexible to account for different parameter settings and failure rate functions. The method is applied to real case data on lift failures. It shows that the method can well handle parameter estimation in the face of missing labels.

关键词： em algorithm lift failures missing labels nonhomogeneous Poisson process reliability statistical inference

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Computational aspects of likelihood-based inference for the univariate generalized hyperbolic distribution

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： van Wyk, Arnold Azzalini, Adelchi Bekker, Andriette Univ Pretoria Fac Nat & Agr Sci Dept Stat ZA-0002 Pretoria South Africa Univ Padua Dipartimento Sci Stat Padua PD Italy

The generalized hyperbolic distribution is among the more often adopted parametric families in a wide range of application areas, thanks to its high flexibility as the parameters vary and also to a plausible stochastic mechanism for its genesis. This high flexibility comes at some cost, however, namely the frequent difficulty of estimating its parameters due to the presence of flat areas of the log-likelihood function, so that selected points of the parameter space, while very distant, can be essentially equivalent as for data fitting. This phenomenon affects not only maximum likelihood estimation, but Bayesian methods too, since the target function is little affected by the introduction of a prior distribution. Our interest focuses in fact on maximum likelihood estimation of the Generalized hyperbolic distribution, working in the univariate case. This paper improves upon currently employed computational techniques by presenting an alternative proposal that works effectively in reaching the global maximum of the likelihood function. The paper further illustrates the above mentioned problems in a number of cases, using both simulated and real data.

关键词： em algorithm Flexible parametric distributions Generalized hyperbolic distributions Maximum likelihood estimation Nelder-Mead simplex method Profile likelihood

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Modeling subpopulations for hierarchically structured data

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STATISTICAL ANALYSIS AND DATA MINING 2024年第1期17卷 e11650-e11650页

作者： Simpson, Andrew Michael, Semhar Borchert, Dylan Saunders, Christopher Tang, Larry South Dakota State Univ Math & Stat Brookings SD USA Univ Cent Florida Dept Stat & Data Sci Orlando FL USA Univ Cent Florida Natl Ctr Forens Sci Orlando FL USA South Dakota State Univ Math & Stat Brookings SD 57007 USA

The field of forensic statistics offers a unique hierarchical data structure in which a population is composed of several subpopulations of sources and a sample is collected from each source. This subpopulation structure creates an additional layer of complexity. Hence, the data has a hierarchical structure in addition to the existence of underlying subpopulations. Finite mixtures are known for modeling heterogeneity;however, previous parameter estimation procedures assume that the data is generated through a simple random sampling process. We propose using a semi-supervised mixture modeling approach to model the subpopulation structure which leverages the fact that we know the collection of samples came from the same source, yet an unknown subpopulation. A simulation study and a real data analysis based on famous glass datasets and a keystroke dynamic typing data set show that the proposed approach performs better than other approaches that have been used previously in practice.

关键词： em algorithm finite mixture models forensic source identification hierarchically structured data likelihood ratio semi-supervised modeling

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